– We show that a 3-qubit system as studied for quantum information purposes can alternatively be used as a thermodynamic machine when externally driven in finite time and interfaced between two split baths. The spins are arranged in a chain where the working spin in the middle exercises Carnot cycles the area of which defines the exchanged work. The cycle orientation (sign of the exchanged work...

Fluctuations of thermodynamic quantities become non-negligible and play an important role when the system size is small. We develop finite-time thermodynamics fluctuations in microscopic heat engines whose environmental temperature mechanical parameter are driven periodically time. Within slow-driving regime, this formalism universally holds a coarse-grained time scale resolution much longer th...

The main motivation of this paper arises from the study of Carnot–Carathéodory spaces, where the class of 1-rectifiable sets does not contain smooth non-horizontal curves; therefore a new definition of rectifiable sets including non-horizontal curves is needed. This is why we introduce in any metric space a new class of curves, called continuously metric differentiable of degree k, which are Hö...

The figure of merit for refrigerators performing finite-time Carnot-like cycles between two reservoirs at temperature T(h) and T(c) (<T(h)) is optimized. It is found that the coefficient of performance at maximum figure of merit is bounded between 0 and (sqrt[9+8ε(c)] - 3)/2 for the low-dissipation refrigerators, where ε(c) = T(c)/(T(h) - T(c)) is the Carnot coefficient of performance for rever...

We show that in any $C^\infty$-rigid Carnot group the sense of Ottazzi - Warhurst, $C^1$-contact maps are automatically smooth.

* Correspondence: yzx8047@yahoo. com.cn School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu 611731, China Full list of author information is available at the end of the article Abstract The purpose of this article, is to study the Dirichlet problems of the sub-Laplace equation Lu + f(ξ, u) = 0, where L is the sub-Laplacian on the Carnot group G and ...

We investigate the energetics of a Brownian motor driven by position-dependent temperature, commonly known as the Büttiker-Landauer motor. Overdamped models (M=0) predict that the motor can attain Carnot efficiency. However, the overdamped limit (M-->0) contradicts the previous prediction due to the kinetic energy contribution to the heat transfer. Using molecular dynamics simulation and numeri...

We investigate the minimal surface problem in the three dimensional Heisenberg group, H , equipped with its standard Carnot-Carathéodory metric. Using a particular surface measure, we characterize minimal surfaces in terms of a sub-elliptic partial differential equation and prove an existence result for the Plateau problem in this setting. Further, we provide a link between our minimal surfaces...

We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum power, we find a universal expression, different from the endoreversible Curzon-Ahlborn efficiency. Our results are illustrated with a simple one-dimensional...

We study partial differential equations of Monge-Ampère type involving the derivates with respect to a family X of vector fields of Carnot type. The main result is a comparison principle among viscosity subsolutions, convex with respect to X , and viscosity supersolutions (in a weaker sense than usual), which implies the uniqueness of solution to the Dirichlet problem. Its assumptions include t...